4) Find f, fy and f, for the followingi) f(x,y,z) = sin 1xyzii) f(x, y,z) = y z In xyiii) f(x,y,z) = e-xyziv) f(x,y,z) = e-²+y²+z*)1v) f(x,y,z) =-Vx²+y² + z²vi) f(x,y,z) = tanh(x + 2y + 3z)vii) f(x,y,z) = sinh(xy – z²)

Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the…

Answered: 4) Find f, fy and f, for the following…

Math

Advanced Math

4) Find f, fy and f, for the following i) f(x,y,z) = sin-xyz ii) f(x, y,z) = y z In xy iii) f(x,y,z) = e-xyz

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x² + 3y , y² -4z , sin(x )cos(y) - z2 ) Now we find div F = ?

Q: r cos(y) + y(e² - 1) x + 0 f (x, y) = ry x = 0.

Q: Show that if sin z| is bounded along the straight line {(x, y): ax - By = 0}, then a = 0, i.e., z…

A: In this question, we have to prove z is in real R. here we use the property of the hyperbolic…

Q: 3. Show that the line integral + 2xy) dx + x² dy + 2xz dz, is independent of path in R3, where C…

A: We will find out the required value.

Q: If z be a differentiable function of x and y and if x = c c cosh u cos v, y = csinh u sin v, then 1…

A: Given that z is a differentiable function of x and y and x=ccosh u cos vy=csinh u sin v We will…

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

Q: 6. The solid bounded by x = y², and x = 8 – 2z2 – y?.

A: To find the triple integral over the given solid bounded by x=y2,x=8-2z2-y2.

Q: By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x…

Q: Suppose that z = x/y, where x and y are differentiable functions of u and v such that x = dx/dv 3, у…

Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

Q: Let f(x, y) = x sin ry. Find: fyy (x, y) fyz(x, y)

A: f(x,y)=xsinxyfx=sinxy+xycosxyfyx=xcosxy+x(cosxy-xysinxy)=2xcosxy-x2ysinxyfy=x2cosxyfyy=-x3sinxy

Q: 9. For F = (x siny, tan(xz),ye¯²), find rot F. A. (-x sec?(xz) - e-zy-1,0, z sec²(xz) – x cos y) B.…

A: the given vector is: F=xsiny,tan(xz),ye-z we have to find rot F.

Q: 18. Ris the annulus in the first and second quadrants bounded by x +y² = 9 and x² + y = 36; 8(x, y)…

Q: Show that f(z) = x ² + y ² where z = x + iy is not analytic anywhere using Cauchy Riemann equations.

A: Cauchy Riemann Equations: Given, f(x+iy)=u(x,y)+iv(x,y) and it should satisfy ∂u∂x=∂v∂y and…

Q: Find the divergence of U = r cos 0 a, - sin 0 ag + 2r² sin 0 2 sin 0 3 sin 0 - r2 2 cos 0 3 cos 0 r2…

Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: t, 01 1 a.) f(t) [m (sh w + (cos w - 1)] cos wt + [[ -[sin sin OLL - cos w + sh w]]sin wet dw - 1…

A: Given the function is ft=t0<t<10t<0, t>1

Q: f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

A: we have to find the approximation of ƒ at the point P = (0, 0, 0, 0). For this we use the proper…

Q: 1) F(x, y, 2) = 3xyi + 2yz j+ 7xz k. 3) F(x, y, z) = 6 e" senyi + 2e* cos yj + 9z k. 5) F(x, y, z) =…

A: We will find out the required value .

Q: Linearizations for Three VariablesFind the linearizations L(x, y, z) of the functions in Exercises…

Q: Bounded by the cylinders z = 2x2, y = x² and the planes z = 0, y = 4

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and u,…

Q: Show that the function f defined on [0, 1] by the conditions f)=2rx when <,r=1, 2, 3,. 1 1=1, 2,…

Q: 9. Evaluate the line integral / (2x – 3y) ds; where C is the line segment from (-1,0) to (0, 1)…

A: 9.

Q: Show that f(z) is differentiable and Evaluate f'(z) if f(z) = u(x,y) + iv(x, y), where %3D u(x, y) =…

Q: sin(xz – 1) In(6+ 3xz + 4yz) = 0 determines z as function of x and y in a neighbourhood of the point…

A: Claim: at (x,y)=(1,1) for the equation Take partial derivative with respect to x Substitute…

Q: 1. Find of/ar, af/ay and of/0z (y- sin(x))² f(x, y) = (r - 1) (y+ 2) + S(1, y) = in(V + y²) + (z² +…

Q: 2. Find the temperature distribution inside a solid parallelepiped with sides (a, b, c) whose faces…

A: Here, uxx + uyy +uzz = 0 .......1 with conditions, ux,y,z,0 = A…

Q: Dete‎rmine if f (x, y) = ={(xsi‎n3y)/(x‎2+y6), (x, ‎y) ≠ (0, ‎0) ={1, (x, y) = (0, 0) is‎…

A: Solution: A graph for a function that's smooth without any holes, jumps, or asymptotes is called…

Q: Show that the line integral is independent of path tan y dr + r sec y dy where C is any path from…

A: Given that ∫C tany dx +x sec2y dyShow that the line integral is independent of path and evaluate the…

Q: Let F(x, y, =) = (6x° In(5y² + 9) + 4=5) i + ( 10yx + 7:)j + (20xz4 + 7y – 37 sin 72) k 5y2 + 9 and…

A: To evaluate

Q: The equations xe" + uz – cos(v) – 2 = 0 and ucos(y) + 6x²v – 4yz² – 1 = 0 can be solved for (u,v) as…

Q: Show that 1 y - X 1. Z-y X-Z = 1. %3D alx-y) alz - x)

Q: Prove that arctan x + arctan y = arctan(x + y) / (1 − xy), xy ≠ 1. Use the…

Q: Compute , F · dS for F = (sin(y), sin(z), yz), S being the rectangle 0 < y < 3,0<z< 6 in the…

A: Given :- ∬S F. dS for F = (sin y , sin z , yz) S being the rectangle 0≤y≤3 , 0≤z≤6 in the yz- plane…

Q: find div and curl F F(x,y,z)= 7y3z2i- 8x2z5j-3xy4k F(x,y,z) = exyi-cosy j +sin2 z k

Q: Consider i = (1,0,0), j= (0, 1, 0), k = (0,0, 1) and, f (x, y) = (x, ²y°, sin x, cos y, xyean +3…

A: We have to make the appropriate selection With the help of following transformation-

Q: Find a potential function for F(x, y, z) = (y² cos z, 2xy cos z, –ry² sin z). %3D COS

Q: The path integral fv· dr, where v = (sin y, x – cos y) and C is the perimeter of the triangle formed…

Q: Find the total differential for the function w = 13z ysin x. dw = 13z ysin xdx-13z sin xdy-26z ysin…

A: Consider the function: Let, w=13z3ysinx=fx,y,z The total differential of the function is given by…

Q: Let f(z) = sin(z'). %3D s'(z) = 3 coslx 3)) 2. 3x cos(X %3D S'(4) = 0

Q: Show that if |sin z| is bounded along the straight line {(x, y) : ax - By = 0}, then a = 0, i.e.,…

A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: 3. A particle is located at a distance x meters from the origin, a force of x +2 newtoms is acting…

A: To find the work done

Q: 2)Evaluate er dA , Ris bounded by y = x2,y 1 3)Evaluate I| Vy2 + 1dA , Ris bounded by x = 4 - y? ,x…

Question

4) Find f, fy and f, for the following
i) f(x,y,z) = sin 1xyz
ii) f(x, y,z) = y z In xy
iii) f(x,y,z) = e-xyz
iv) f(x,y,z) = e-²+y²+z*)
1
v) f(x,y,z) =-
Vx²+y² + z²
vi) f(x,y,z) = tanh(x + 2y + 3z)
vii) f(x,y,z) = sinh(xy – z²)

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Hyperbolas$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

△XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1). Which of the following can be used to prove that △XYZ is isosceles?
A triangle is bounded by the lines y = x, y = -x, and y = 1 When setting up an intergral to find mass or inertia or whatever, why can I not set it up as integral(1, -1) integral(1, x) dydx and instead need to set it up as integral(1, 0) integral(y, -y) dxdy
How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help in advance. :)
what local linearizatoin of the function f(x,y) sin(xy) + cos(x/y) at (pie/4, 1) (show all steps please)
Integrate f(x, y, z) = x2 -y + z over the line segments from (0, 0, 0) to (1, 1, 0) and then to the point (1, 1, 1).
Bounded by the cylinder x 2 + y 2 = 1 and the planes y= z x =0 z= 0 in the first octant
By writing the ODEs in their normal form near the bifurcation point show that (a) ˙x = 1 + rx x cos(x) + sin(r) undergoes a saddle-node bifurcation at (r∗ , x∗ ) = (0, 0), (b) ˙x = (r2 2 r + 1)(x + x3) ) ln(1 + x) undergoes a transcritical bifurcation at (r∗ , x∗ ) = (1, 0). Please specify the order of the approximation as an error in ε > 0 and the corresponding size of r, x, e.g. |x - x∗| < ε.
Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x,y,z) so that
. Let x, y and z be the angles of a triangle. Determine the maximum valueof f(x, y, z) = sin x sin y sin z.
Can you explain how we get for the red lines: x = a-z , z = a-y , z = 4-x-y, y = a -x and show what is the plane a-x-y-z = 0 since I do not understand it, and how I find the limits of integration